Lesson a: Newton's First Law of Motion
What is Newton's First Law of Motion?
- An object at rest stays at rest and an object in motion stays in motion (with the same speed and same direction) unless acted upon by an unbalanced force.
How can this be applied to everyday life?
- Example: driving with a cup of coffee: the car makes a short stop, so the coffee spills since it's still moving.
- Example: the car makes a short stop and the passenger slides forward (but it stopped by the seatbelt). The person remains in motion even though the car has stopped. The seatbelt is the unbalanced that brings the person from a state of motion to one of rest. Lesson b: Inertia and Mass
What is inertia?
- Inertia is the resistance an object has to a change in its state of motion.
Describe Galileo's concept of inertia.
- Moving objects eventually stop due to friction. If friction could be eliminated, an object rolling down a slope would stop when it reaches the original height (back up) (initial height=final height). If the opposing incline was not an incline (horizontal) the object would continue moving forever (if friction was absent).
Explain Newton's continuation of this theory.
- A force is not needed to keep an object in motion- rather, it can stop the motion (friction).
What is mass in relation to inertia?
- The tendency of an object to resist changes in its state of motion varies with mass.
- Mass is the quantity that solely depends upon the inertia of an object.
- The more inertia an object has, the more mass it has (more massive objects tend to resist changes in state of motion more). Lesson c: State of Motion
What is an objects "state of motion"?
- The state of motion of an object is defined by its velocity- the speed with a direction.
- New definition of inertia: tendency of an object to resist changes in it's velocity (or resist accelerations). Lesson d: Balanced and Unbalanced Forces
What is the difference between balanced and unbalanced forces? Give example of each.
- Balanced Forces: a book resting on a table (table pushes up on the book, gravity pulls down on it) the forces on the book are balanced: equal magnitude and opposite directions. So the book is at equilibrium. No unbalanced force acting upon it so it maintains its state of motion.
- Unbalanced Forces: a book sliding across a table from left to right. Gravity pulls downwards on the book, the table pushes upwards on the book, and friction between the table and book exerts a leftward force (on the book). So, there are unbalanced forces acting on the book (since there's no force present to balance the force of friction). So, the book changes its state of motion. It's not at equilibrium so it accelerates. Summary of Lesson 1 (a-d): - Objects at rest stay at rest, objects in motion stay in motion unless acted upon by an unbalanced force. This explains the concept of inertia, which was first introduced by Galileo and then built upon by Newton. Forces balance each other when they have the same magnitude and are in opposite directions; objects that are accelerating have unbalanced forces.
Lesson 2: a-d
Lauren Kostman
November 15, 2011
Lesson a: The Meaning of Force
What is the meaning of force?
- A force is a push or pull upon an object from the object's interaction with another object.
- There are 2 kinds of forces:
1.) Contact Forces (result when 2 interacting objects are seen to be physically contacting each other).
2.) Action-at-a-Distance Forces (result when 2 interacting objects are not in physical contact with each other, yet are ale to exert a push or pull despite their physical separation).
- Forces are measured in Newtons (N). (1)N=1kg*(m/s^2) Lesson b: Types of Forces
What are the different types of forces? Describe each of them.
- Gravity Force (weight): force that pulls the object downwards towards the center of the earth. w=m*g.
- Normal Force: support force exerted on an object that is in contact with another stable object.
- Friction Force: exerted by a surface as an object moves across it (or tries to do so).
- There are 2 kinds:
1.) Sliding (results when an object slides across a surface).
2.) Static (results when the surfaces of two objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object).
- Tension Force: transmitted through a rope when it's pulled tight by forces acting form opposite ends.
What's the difference between mass and weight?
- Weight (N)= the force of gravity acting upon an object (depends on the planet).
- Mass (kg)= the amount of matter that is contained by the object. Lesson c: Drawing Free-Body Diagrams
How does one draw a free-body diagram?
- FBD are used to show relative magnitude and direction of all forces acting upon an object in a given situation.
- Determine the forces acting upon the object; use arrows the place these forces on the system (don't include environment). Label arrows with the appropriate symbol for the given type of force. Lesson d: Determining the Net Force
Explain how to determine the net force.
- The net force is the vector sum of all the forces that act upon an object. A force is a vector and 2 forces of equal magnitude and opposite direction will cancel each other out. Summary of Lesson 2 (a-d): There are many kinds of forces (push/pull due to interaction between 2 objects). Such forces can be depicted on a free body diagram, where arrows are used to show magnitude and direction of each kind of force present in a given situation. The net force can be determined by adding up the vectors; vectors with the same magnitude in opposite directions cancel each other out.
Lesson 3: a, b
Lauren Kostman
November 16, 2011
Lesson a: Newton's Second Law
What does Newton's Second Law of Motion state?
- It states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
a=Fnet/m or Fnet=m*a
- Acceleration is directly proportional to net force.
- Acceleration is inversely proportional to mass.
- A unit of force (newton, N) is equal to a unit of mass times a unit of acceleration. 1N=1kg* (m/s^2) Lesson b: The Big Misconception
What is the "big misconception"?
- A misconception is the idea that sustaining motion requires a continued force; this belief is wrong!
*Forces are NOT required to keep an object in motion!
- Newton's laws declare that a net force (unbalanced force) causes an acceleration, which is in the same direction as the net force. Summary of Lesson 3 (a,b): Newton's Second Law pertains to the behavior of objects for which all existing forces are NOT balanced.There is acceleration, which depends directly on the net force, and inversely on the mass of the object. Many people believe that forces are required to keep objects in motion, but this is false! It's just a common misconception.
Force and it's Representation
Lauren Kostman
12/5/11
Sliding versus Static Friction:
Sliding Friction
Occurs when an object slides across a surface
Example: box pushed across the floor
Floor surface offers resistance to the movement of the box (friction)
Formula: (sliding) f= µ*N
Static Friction
Occurs when the surfaces of 2 objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object
Example: you try to push a large box across the floor, but it remains in place (due to static friction)
Relationship: (static) f=µ(static)*N
Lesson 3: a-f
Lauren Kostman
12/6/11
Lesson a:
How do you add forces?
- The purpose of adding force vectors is to the determine the net force acting on an object.
-The net force is the sum of all the forces; using the corresponding acceleration, add the forces together. Lesson b:
What does the phrase, "the resolution of forces" mean?
- A single force can be resolved into 2 components- one directed upwards and the other directed rightwards.
- Each component describes the influence of that chain in a given direction.
- Use trigonometric functions (SOH CAH TOA) to determine the components of a certain force. Lesson c:
What is static equilibrium?
- Equilibrium means the forces are balanced, but not necessarily equal (left/right must be equal, and up/down must be equal).
- When at equilibrium, the net force is zero and the acceleration is 0.
- Objects at equilibrium are at rest or at constant speed.
- Objects at rest that are in a state of equilibrium are at "static equilibrium" (static= rest). Lesson d:
How does one solve a net-roce acceleration problem with an applied force directed at an angle to the horizontal?
- Split the force vector into 2 components.
- Use sin/cos of the given angle and solve like any other problem. Lesson e:
How does one solve a problem on an inclined plane?
- There are always at least 2 forces acting upon any object that's positioned on an incline plane- normal and weight.
- Weight acts in a downward direction, yet the normal force acts in a direction perpendicular to the surface.
- Split the weight into x and y components that are perpendicular to the surface using sin/cos.
- Without friction and other forces: a=g*sin(theta). Lesson f:
How does one solve two body problems (2 masses connected by string)?
- Draw out free body diagrams.
- Apply Newton's second law (net force= mass* acceleration).
- Apply Newton's third law (action-reaction), which states that the force object 1 exerts on object 2 is equal and opposite to the force object 2 exerts on object 1.
Table of Contents
Chapter 4: Newton's Laws of Motion
Lesson1: a-d
Lauren KostmanNovember 14, 2011
Lesson a: Newton's First Law of Motion
What is Newton's First Law of Motion?
- An object at rest stays at rest and an object in motion stays in motion (with the same speed and same direction) unless acted upon by an unbalanced force.
How can this be applied to everyday life?
- Example: driving with a cup of coffee: the car makes a short stop, so the coffee spills since it's still moving.
- Example: the car makes a short stop and the passenger slides forward (but it stopped by the seatbelt). The person remains in motion even though the car has stopped. The seatbelt is the unbalanced that brings the person from a state of motion to one of rest.
Lesson b: Inertia and Mass
What is inertia?
- Inertia is the resistance an object has to a change in its state of motion.
Describe Galileo's concept of inertia.
- Moving objects eventually stop due to friction. If friction could be eliminated, an object rolling down a slope would stop when it reaches the original height (back up) (initial height=final height). If the opposing incline was not an incline (horizontal) the object would continue moving forever (if friction was absent).
Explain Newton's continuation of this theory.
- A force is not needed to keep an object in motion- rather, it can stop the motion (friction).
What is mass in relation to inertia?
- The tendency of an object to resist changes in its state of motion varies with mass.
- Mass is the quantity that solely depends upon the inertia of an object.
- The more inertia an object has, the more mass it has (more massive objects tend to resist changes in state of motion more).
Lesson c: State of Motion
What is an objects "state of motion"?
- The state of motion of an object is defined by its velocity- the speed with a direction.
- New definition of inertia: tendency of an object to resist changes in it's velocity (or resist accelerations).
Lesson d: Balanced and Unbalanced Forces
What is the difference between balanced and unbalanced forces? Give example of each.
- Balanced Forces: a book resting on a table (table pushes up on the book, gravity pulls down on it) the forces on the book are balanced: equal magnitude and opposite directions. So the book is at equilibrium. No unbalanced force acting upon it so it maintains its state of motion.
- Unbalanced Forces: a book sliding across a table from left to right. Gravity pulls downwards on the book, the table pushes upwards on the book, and friction between the table and book exerts a leftward force (on the book). So, there are unbalanced forces acting on the book (since there's no force present to balance the force of friction). So, the book changes its state of motion. It's not at equilibrium so it accelerates.
Summary of Lesson 1 (a-d):
- Objects at rest stay at rest, objects in motion stay in motion unless acted upon by an unbalanced force. This explains the concept of inertia, which was first introduced by Galileo and then built upon by Newton. Forces balance each other when they have the same magnitude and are in opposite directions; objects that are accelerating have unbalanced forces.
Lesson 2: a-d
Lauren KostmanNovember 15, 2011
Lesson a: The Meaning of Force
What is the meaning of force?
- A force is a push or pull upon an object from the object's interaction with another object.
- There are 2 kinds of forces:
1.) Contact Forces (result when 2 interacting objects are seen to be physically contacting each other).
2.) Action-at-a-Distance Forces (result when 2 interacting objects are not in physical contact with each other, yet are ale to exert a push or pull despite their physical separation).
- Forces are measured in Newtons (N). (1)N=1kg*(m/s^2)
Lesson b: Types of Forces
What are the different types of forces? Describe each of them.
- Gravity Force (weight): force that pulls the object downwards towards the center of the earth. w=m*g.
- Normal Force: support force exerted on an object that is in contact with another stable object.
- Friction Force: exerted by a surface as an object moves across it (or tries to do so).
- There are 2 kinds:
1.) Sliding (results when an object slides across a surface).
2.) Static (results when the surfaces of two objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object).
- Tension Force: transmitted through a rope when it's pulled tight by forces acting form opposite ends.
What's the difference between mass and weight?
- Weight (N)= the force of gravity acting upon an object (depends on the planet).
- Mass (kg)= the amount of matter that is contained by the object.
Lesson c: Drawing Free-Body Diagrams
How does one draw a free-body diagram?
- FBD are used to show relative magnitude and direction of all forces acting upon an object in a given situation.
- Determine the forces acting upon the object; use arrows the place these forces on the system (don't include environment). Label arrows with the appropriate symbol for the given type of force.
Lesson d: Determining the Net Force
Explain how to determine the net force.
- The net force is the vector sum of all the forces that act upon an object. A force is a vector and 2 forces of equal magnitude and opposite direction will cancel each other out.
Summary of Lesson 2 (a-d):
There are many kinds of forces (push/pull due to interaction between 2 objects). Such forces can be depicted on a free body diagram, where arrows are used to show magnitude and direction of each kind of force present in a given situation. The net force can be determined by adding up the vectors; vectors with the same magnitude in opposite directions cancel each other out.
Lesson 3: a, b
Lauren Kostman
November 16, 2011
Lesson a: Newton's Second Law
What does Newton's Second Law of Motion state?
- It states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
a=Fnet/m or Fnet=m*a
- Acceleration is directly proportional to net force.
- Acceleration is inversely proportional to mass.
- A unit of force (newton, N) is equal to a unit of mass times a unit of acceleration. 1N=1kg* (m/s^2)
Lesson b: The Big Misconception
What is the "big misconception"?
- A misconception is the idea that sustaining motion requires a continued force; this belief is wrong!
*Forces are NOT required to keep an object in motion!
- Newton's laws declare that a net force (unbalanced force) causes an acceleration, which is in the same direction as the net force.
Summary of Lesson 3 (a,b):
Newton's Second Law pertains to the behavior of objects for which all existing forces are NOT balanced.There is acceleration, which depends directly on the net force, and inversely on the mass of the object. Many people believe that forces are required to keep objects in motion, but this is false! It's just a common misconception.
Force and it's Representation
Lauren Kostman12/5/11
Sliding versus Static Friction:
Lesson 3: a-f
Lauren Kostman12/6/11
Lesson a:
How do you add forces?
- The purpose of adding force vectors is to the determine the net force acting on an object.
-The net force is the sum of all the forces; using the corresponding acceleration, add the forces together.
Lesson b:
What does the phrase, "the resolution of forces" mean?
- A single force can be resolved into 2 components- one directed upwards and the other directed rightwards.
- Each component describes the influence of that chain in a given direction.
- Use trigonometric functions (SOH CAH TOA) to determine the components of a certain force.
Lesson c:
What is static equilibrium?
- Equilibrium means the forces are balanced, but not necessarily equal (left/right must be equal, and up/down must be equal).
- When at equilibrium, the net force is zero and the acceleration is 0.
- Objects at equilibrium are at rest or at constant speed.
- Objects at rest that are in a state of equilibrium are at "static equilibrium" (static= rest).
Lesson d:
How does one solve a net-roce acceleration problem with an applied force directed at an angle to the horizontal?
- Split the force vector into 2 components.
- Use sin/cos of the given angle and solve like any other problem.
Lesson e:
How does one solve a problem on an inclined plane?
- There are always at least 2 forces acting upon any object that's positioned on an incline plane- normal and weight.
- Weight acts in a downward direction, yet the normal force acts in a direction perpendicular to the surface.
- Split the weight into x and y components that are perpendicular to the surface using sin/cos.
- Without friction and other forces: a=g*sin(theta).
Lesson f:
How does one solve two body problems (2 masses connected by string)?
- Draw out free body diagrams.
- Apply Newton's second law (net force= mass* acceleration).
- Apply Newton's third law (action-reaction), which states that the force object 1 exerts on object 2 is equal and opposite to the force object 2 exerts on object 1.